13. PowerLoom Grammar

The syntax of PowerLoom is described below using a modified BNF notation adapted from the KIF specification.

13.1 Alphabet

We distinguish between terminals, which are part of the language, and nonterminals. All nonterminals are bracketed as follows <nonterminal>. Squared brackets means zero or one instances of the enclosed expression; <nonterminal>* means zero or more occurrences and <nonterminal>+ means one or more occurrences of <nonterminal>. The notation <nonterminal1> - <nonterminal2> refers to all of the members of <nonterminal1> except for those in <nonterminal2>.

A word is a contiguous sequence of characters, which include all upper case letters, lower case letters, digits and alpha characters (ASCII character set from 93 to 128) excluding some special characters like white spaces, single and double quotes and brackets.

<word> ::= a primitive syntactic object

Special words are those who refer to a variable. All variables are preceded by a question mark.

<indvar> ::= a word beginning with the character ?

A string <string> is a character sequence including words plus all special charcters (except double quotes) enclosed in double quotes. A double quote can be included in a string if it is preceeded by the escape character ’\’.

13.2 Grammar

Legal expressions in PowerLoom are forms, which are either a statement or a definition, described in more detail below.

<form> ::= <statement> | <definition>

13.2.1 Constants and Typed Variables

The language consists of several groups of operators, defined as follows:

<termop> ::= listof | setof | the | setofall | kappa

<sentop> ::= = | /= | not | fail | and | or | forall | exists
               | <= | => | <=> |<<= | =>> | <~ | ~> | <<~ | ~>>

<defop> ::= defconcept | deffunction | defrelation | defrule |
              :documentation | :-> |
              :<= | :=> | :<<= | :=>> |
              :<=> | :<=>> :<<=> | :<<=>> | := |
              :axioms

<operator> ::= <termop> | <sentop> | <defop>

All other words are constants (words which are not operators or variables):

<constant> ::= <word> - <indvar> - <operator>

Semantically, there are different categories of constants — Concept constants <conceptconst>, Function constants <funconst>, Relation constants <relconst>, Rule constants <ruleconst> and Logical constants <logconst>. The differences between these categories are entirely semantic. However, some operators will only accept specific constants.

In contrast to the specification of KIF3.0, PowerLoom supports a typed syntax. Therefore, variables in quantified terms and sentences can appear either typed or untyped, as follows:

<vardecl> ::= (<indvar> <constant>) | <indvar>

13.2.2 Terms

Terms are used to denote objects in the world being described:

<term> ::= <indvar> | <constant> | <funterm> | <listterm> | <setterm> |
             <quanterm>

<listterm> ::= (listof <term>*)

<setterm> ::= (setof <term>*)

<funterm> ::= (<funconst> <term>+)

Note: Zero arguments are allowed for <funterm> in KIF3.0: <term>*

<quanterm> ::= (the <vardecl> <sentence>) |
                 (setofall <vardecl> <sentence>) |
                 (kappa {<vardecl> | (<vardecl>+)} <sentence>) |
                 (lambda {<vardecl> | (<vardecl>+)} <term>)

Note: KIF3.0 allows <term> instead of <vardecl> for setofall. No <quanterm> as well as no <setterm> in core of KIF as a result of descision 95-3 (March 1995).

13.2.3 Sentences

Sentences are used to express propositions about the world:

<sentence> ::= <constant> | <equation> | <inequality> |
                 <relsent> | <logsent> | <quantsent>

<equation> ::= (= <term> <term>)

<inequality> ::= (/= <term> <term>)

<relsent> ::= (<constant> <term>+)

Note: Zero arguments allowed in KIF3.0 for <relsent> (<term>*). <funconst> is currently not allowed in PowerLoom (use (= <funterm> <term>) instead).

<logsent> ::= (not <sentence>) |
                (fail <sentence>) |
                (and <sentence>*) |
                (or <sentence>*) |
                (=> <sentence>* <sentence>) | (=>> <sentence>* <sentence>) |
                (<= <sentence> <sentence>*) | (<<= <sentence> <sentence>*) |
                (~> <sentence>* <sentence>) | (~>> <sentence>* <sentence>) |
                (<~ <sentence> <sentence>*) | (<<~ <sentence> <sentence>*)

<quantsent> ::= (forall {<vardecl> | (<vardecl>+)} <sentence>) |
                  (forall {<vardecl> | (<vardecl>+)} <sentence> <sentence>) |
                  (exists {<vardecl> | (<vardecl>+)} <sentence>)

13.2.4 Definitions

PowerLoom supports two distinct categories of definitions — relation definitions (including concept and function definitions) and rule definitions. A relation definition introduces a new logical constant, and states some facts about that constant (e.g., who its parents are in a subsumption taxonomy). A rule definitions binds a new constant to a proposition (so that the constant denotes the proposition) and asserts the truth of that proposition. Usually, the proposition asserted by a defrule is an implication. The assertional truth of a proposition defined by a rule can be altered by asserting or retracting the constant that denotes the proposition.

<keyword-option> ::= <keyword> <word>
<definition> ::= <reldefinition> | <objdefinition> | <ruledefinition>

<reldefinition> ::= 
 (defconcept <conceptconst> <vardecl>
    [:documentation <string>]
    [:<= <sentence>] | [:=> <sentence>] |
    [:<<= <sentence>] | [:=>> <sentence>] | 
    [:<=> <sentence>] | [:<=>> <sentence>] | [:<<=> <sentence>] |
    [:<<=>> <sentence>] |
    [:axioms {<sentence> | (<sentence>+)}] |
    [<keyword-option>*])
 |
 (deffunction <funconst> (<vardecl>+)
    [:documentation <string>]
    [:-> <vardecl>]
    [:<= <sentence>] | [:=> <sentence>] |
    [:<<= <sentence>] | [:=>> <sentence>] | 
    [:<=> <sentence>] | [:<=>> <sentence>] | [:<<=> <sentence>] |
    [:<<=>> <sentence>] |
    [:axioms {<sentence> | (<sentence>+)}]
    [<keyword-option>*])
 |
 (defrelation <relconst> (<vardecl>+)
    [:documentation <string>]
    [:<= <sentence>] | [:=> <sentence>] |
    [:<<= <sentence>] | [:=>> <sentence>] | 
    [:<=> <sentence>] | [:<=>> <sentence>] | [:<<=> <sentence>] |
    [:<<=>> <sentence>] |
    [:axioms {<sentence> | (<sentence>+)}]
    [<keyword-option>*])

<objdefinition> ::= (defobject <constant>
                       [:documentation <string>]
                       [<keyword-option>*])

<ruledefinition> ::= (defrule <constant> <sentence>
                       [:documentation <string>]
                       [<keyword-option>*])

<ruledefinition> ::= (defrule <ruleconst> <sentence>)

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